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JEE Main 2021 (27 Aug, Shift 2) · Combination of Lenses

Combination of Lenses question from JEE Main 2021 (27 Aug, Shift 2)

Q47JEE Main 2021 · 27 AUG · SHIFT 2Medium

Combination of Lenses

Curved surfaces of a plano-convex lens of refractive index $\mu$ 1 and a plano-concave lens of refractive index $\mu$ 2 have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

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Answer: (b)

Plano-convex ( $\mu_1$ ) and plano-concave ( $\mu_2$ ) of the same $R$ in contact:
$\frac{1}{f} = \frac{\mu_1-1}{R} - \frac{\mu_2-1}{R} = \frac{\mu_1-\mu_2}{R}$
$\frac{R}{f} = \mu_1 - \mu_2$
So the answer is (b) $\mu_1 - \mu_2$ .

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